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Centered tetrahedral number

  • Last Updated : 19 Jul, 2021

We are given integer n, we need to find n-th centered tetrahedral number.
Description: The centered tetrahedral number is a centered figurate number that represents a tetrahedron.
Tetrahedral Numbers: A number is termed as a tetrahedral number if it can be represented as a pyramid with a triangular base and three sides, called a tetrahedron. The nth tetrahedral number is the sum of the first n triangular numbers
The first few centered tetrahedral number series are: 
1, 5, 15, 35, 69, 121, 195, 295, 425, 589……………………….
Mathematical nth Term of centered tetrahedral number:
 

\\ CTh_{n} = \frac{(2n+1)(n^2+n+3)}{3}

Examples :
 

Input : n = 3
Output : 35

Input : n = 9
Output : 589

Below is the implementation of above formula. 
 

C++




// C++ Program to find nth
// Centered tetrahedral number
#include <bits/stdc++.h>
using namespace std;
 
// Function to find centered
// Centered tetrahedral number
int centeredTetrahedralNumber(int n)
{
    // Formula to calculate nth
    // Centered tetrahedral number
    // and return it into main function.
    return (2 * n + 1) * (n * n + n + 3) / 3;
}
 
// Driver Code
int main()
{
    int n = 6;
 
    cout << centeredTetrahedralNumber(n);
 
    return 0;
}

Java




// Java Program to find nth Centered
// tetrahedral number
import java.io.*;
 
class GFG {
 
    // Function to find centered
    // Centered tetrahedral number
    static int centeredTetrahedralNumber(int n)
    {
         
        // Formula to calculate nth
        // Centered tetrahedral number
        // and return it into main function.
        return (2 * n + 1) * (n * n + n + 3) / 3;
    }
     
    // Driver Code
 
 
    public static void main (String[] args)
    {
        int n = 6;
 
        System.out.println(
                   centeredTetrahedralNumber(n));
    }
}
 
// This code is contributed by anuj_67.

Python3




# Python program to find nth
# Centered tetrahedral number
 
# Function to calculate
# Centered tetrahedral number
 
def centeredTetrahedralNumber(n):
 
    # Formula to calculate nth
    # Centered tetrahedral number
    # and return it into main function
     
    return (2 * n + 1) * (n * n + n + 3) // 3
 
# Driver Code
n = 6
print(centeredTetrahedralNumber(n))
                     
# This code is contributed by ajit                

C#




// C# Program to find nth Centered
// tetrahedral number
using System;
 
class GFG {
 
    // Function to find centered
    // Centered tetrahedral number
    static int centeredTetrahedralNumber(int n)
    {
         
        // Formula to calculate nth
        // Centered tetrahedral number
        // and return it into main function.
        return (2 * n + 1) * (n * n + n + 3) / 3;
    }
     
    // Driver Code
 
 
    public static void Main ()
    {
        int n = 6;
 
        Console.WriteLine(
                centeredTetrahedralNumber(n));
    }
}
 
// This code is contributed by anuj_67.

PHP




<?php
// PHP Program to find nth
// Centered tetrahedral number
 
// Function to find centered
// Centered tetrahedral number
function centeredTetrahedralNumber($n)
{
    // Formula to calculate nth
    // Centered tetrahedral number
    // and return it into main function.
    return (2 * $n + 1) *
           ($n * $n + $n + 3) / 3;
}
 
// Driver Code
$n = 6;
 
echo centeredTetrahedralNumber($n);
 
// This code is contributed by anuj_67.
?>

Javascript




<script>
 
// Javascript program to find nth Centered
// tetrahedral number
 
// Function to find centered
// Centered tetrahedral number
function centeredTetrahedralNumber(n)
{
     
    // Formula to calculate nth
    // Centered tetrahedral number
    // and return it into main function.
    return (2 * n + 1) * (n * n + n + 3) / 3;
}
 
// Driver Code
 
// Given Number
var n = 6;
 
document.write(centeredTetrahedralNumber(n));
 
// This code is contributed by Kirti
     
</script>
Output : 
195

 

Time Complexity: O(1)
Auxiliary Space: O(1)

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